Consider proportional only control of the level control system in Fig. 11.16. The level transmitter has a span of 10 ft. and a zero of 15 ft. Recall that the standard instrument ranges are 4 to 20 mA and 3 to 15 psia. The nominal design conditions are h = 20 ft. The controller has a gain of 5 while the gain for the control valve is K_v = 0.4 cfm/psi, respectively. The time constant for the tank is Ï„ = 5 min. After the set-point is changed from 20 to 22 ft, the tank level eventually reaches a new steady-state value of 21.92 ft.
(a) What is the offset?
(b) What are the gains K_mand K_pin Fig. 11.16? (Give their units also)
(c) How could the controller be modified to obtain zero offset?

Qi [m/min] ' Hap P' [m] K, ts + 1 G(s) K, [%] [%] [%] [psi) [m3/min] [m] ' H [%] [m] Figure 11.16 Block diagram for level control system.